Mull this one carefully. Say a mammogram is 90 percent accurate at spotting patients with breast cancer, and 93 percent accurate at spotting those without breast cancer. Breast cancer afflicts 0.8 percent of women tested. Your mammogram comes back positive. How likely is it that you have breast cancer?
Less than 10 percent, says “The Numbers Game” (Gotham), a chatty, brief, brightly informative and quite possibly essential book by a pair of blokish Brits (not statisticians or mathletes). An alternate title might be “When Journalists Do Math”; “Numbers,” published to huzzahs in the UK last year, is a genteel carpet-bombing of alternately hysterical and gullible journalists who misread numbers.
Authors Michael Blastland and Andrew Dilnot, who developed the book from a BBC radio show, break down the breast cancer case as follows. Of 1,000 women, eight have cancer. Seven of them will find their test coming back positive. The remaining 992 women don’t have cancer, but 7 percent – almost 70 of them – will get a false positive result. Of 77 positive results, only seven are accurate. Don’t worry if you got the question wrong (or rather do worry, a lot), because only two of 24 physicians passed the quiz.
Asking simple questions such as “Is that a big number” (sometimes six is but a trillion is not), the authors rip through misconceptions about numbers while betraying no political bias. Readers from left and right will find many an a-ha moment to savor, and the book is so brisk and compact (it bills itself as “the Strunk & White of Statistics”) that it’s going to be irresistible to bloggers.
Putting risks in percentage terms is one way to inflate them into front-page scares: If a possibility rises from a one-in- a-million shot to two-in-a-million, 100 percent. The American Institute of Cancer Research told everyone to stop eating all processed meat after a 21 percent increase in colon cancer was linked to bacon consumption. Calm down, though: typically, five men in a hundred get colon cancer in a lifetime. About six would if they all ate two extra slices of bacon a day. The authors actually praise the sassy British tabloid The Sun (which like this paper is owned by News Corp.) for dampening the AICR’s warning, saying “it beat the serious newspapers for intelligible reporting of the risks, being one of the very few to make it clear how many people could be affected.”
When British consumer debt reached one trillion pounds, the media went into a swoon, but consider a more common-sense interpretation: your life. “How much did you owe at age fifteen? Four dollars and twenty cents – to your brother – how prudent.” Then “when you subsequently took out a mortgage, why, your debts probably reached a record! This must have been, obviously, the most miserable, destitute moment of your life, as you pined for the financial circumstances of a fifteen-year-old once more.” Isn’t increased debt often a sign of a better life?
The authors are amused at the “astonishing” number of headlines that contain the scare words “one in four” – such as some twaddle blasted all over the UK media (London newspapers, even the “quality” ones, speak in a shrieking, disaster-warning tone that makes ours look shy by comparison) about the number of British youths who are criminals. It turned out that “assault” was defined all the way down to kids pushing or grabbing in the lunch line. Environmental cancer clusters, food toxicity and the “Sports Illustrated Curse” all get a razzing.
The 2003 community uprising that led to a cellphone tower being sabotaged in an English village followed nine cancer diagnoses in 20 households located within 500 yards of the tower. While taking care not to dismiss the villagers’ assumptions about linkage between the tower and the cancer, Blastland and Dilnot compare the distribution of cancer cases to what happens when you toss a fistful of rice in the air. The grains on the floor do not take the trouble to spread themselves out at an equal distance from one another. Here and there you will find dense clusters.
Sports-radio hosts and listeners, please read the pages on fl ipping coins before your next soliloquy on how this or that team or player is “hot” or “cold.” When flipping a coin 30 times, the same side will commonly land up four, five or six times in a row. It doesn’t mean anything, Vinnie from Queens. Stop poring over the tables and go tell your wife she looks pretty.
It takes even less familiarity with statistics to be stunned by the public policy implications in a simple question about abortion figures. Asked in an experiment to guess how many abortions occur in the US for every million live births, students gave a wide range of answers. At the middle of the range was an estimate of 5,000. That figure is so far from the correct answer – 335,000 – that, in the words of the physicist Wolfgang Pauli, it is “not even wrong.” Blastland and Dilnot report that being asked to guess before learning the correct answer leads to a greater sense of surprise, and students in the experiment became much more supportive of abortion restrictions. “Accurate data does matter to people,” the authors rule. Makers of campaign advertisements, take note.
A chapter on how political pressure to lower waiting times in socialized Britain led to a fiddling of numbers (that masked the actual increase) and No Child Left Behind mandates led to similar legerdemain here illustrates how the stats that matter most are the ones most likely to be corrupted. Those who suspect Joe the Plumber of being a plutocrat in a utility belt will take satisfaction in a chapter about misuse of terms like “average” and “middle class.” You have more than the average number of feet, did you know that? How couldn’t you, given that some people have none and drag the average below two? To be less frivolous, if you have average income you are actually in the top 20 percent of wage earners. A few zillionaires hoist the average up.
Even senior civil servants polled in Britain in 2005 (and given multiple choices!) proved utterly bereft of a clue when asked what income level lands a childless Brit couple in the top 10 percent of earners. A typical bit of waggishness puts their responses in chart form: 3 percent of respondents said 100,000 pounds (classified as “disgraceful” on the chart); 19 percent said 80,000 pounds (“appalling”), 21 percent said 65,000 pounds (“embarrassing”), 48 percent said 50,000 pounds (“wrong”) and only 10 percent gave the correct answer: a mere 35,000 pounds. (In the US, as of 2007, the equivalent figure was a much more robust $130,000, which carries its own implications about the long-term effects of a mildly socialized economy.)
The flip side of not understanding how little it takes to be rich, though, is that people don’t realize how much of the tax burden the rich already carry. When asked what percentage of income tax is paid by the top 1 percent, the most common reply given by British bureaucrats was 11 percent. Another 38 percent of respondents thought the share was either 8 percent or 5 percent. In reality, the richest one percent pay 21 percent of all income tax in the UK – and in the supposedly regressive US, it’s 35 percent. (Hands up, all those who think American government workers are a lot brighter than their cousins across the pond. Anyone? Anyone?)
Nearly 100 percent of the statistics presented here are dodgy, so the book stands in danger of being abused by anti-intellectuals who may conclude that we should never trust official numbers or make too much of unlikely coincidences.
Take the case of the cellphone tower and the cancer. Should we brush off the village’s belief that the tower caused the cancer? No. Really, all the authors ask is for journalists, bloggers and pundits to resist snap judgments, to dig deeper than the press release, to be smarter.
Nice, but you might as well ask the hackocracy to give up coffee and booze.
280 days: The length of an average pregnancy, as decided by an 1812 study and never changed by modern medicine. The problem is, by inducing longer births, doctors actually help encourage that average; no one is sure what the true average would be. Even with inductions, though, most pregnancies last three days longer – 283. By giving women an artificial “due date,” doctors may make them unduly worried when they go past it.
21%:An extra ounce of bacon a day increased the chance of colon cancer by this much in men, according to the American Institute of Cancer Research. While a huge percentage, it neglected to mention what that increase meant in raw numbers. Turns out, five men out of 100 get colorectal cancer in their lifetime. Bacon-eating increased it to six.
.001%: The number of people who would ordinarily get acoustic neuroma. What’s that? A tumor near the ear. In 2005, media reported that the chance of such tumors “doubled” by using cellphones. Almost no one reported the baseline number. In truth, “doubled” meant that now two in 100,000 would get them, as compared to one in 100,000.
32: Average lifespan of a man in Swaziland, the lowest in the world, according to the CIA’s Wolrd Factbook. The problem, again, is average. Most adult males there live much longer – it’s the large infancy mortality rate that drags down the average.
$1,800: Amount the average American’s taxes would increase if his cuts were rescinded, George Bush argued this year. This is true, but averages can be skewed by a large sample that includes outsize earners – in fact, 80 percent would not have seen that big an increase.
65 lbs: Amount of cooked potatoes a person would have to eat every day for years to ingest toxic levels of acrylamide. Yet in 1997, when Swedish researchers found acrylamide in some cooked foods, it set off a health scare. Reports of dangers often fail to mention the dosage needed.
4 out of 5: Number of Americans who call themselves “middle class.” In fact, the middle 20 percent of households in the US make between $38,000 and $60,000 a year. The middle 60 percent make between $20,000 and $97,000.
70%: Packages that were mailed in the original “six degrees of separation” experiment that never reached the right person. Though packages that did arrive had, on average, six steps to reach the desired recipient, such a large number of undelivered items makes the conclusion highly dubious.
7%: How much speed-cameras really decreased accidents, according to one British study. The government had originally claimed a 35 percent reduction, but sometimes accidents just drop on their own, a “regression to the mean.” In studying the effects of initiatives like the smoking ban, one can’t attribute every decrease to it; numbers always change.
1: Number of children sampled in a study about how many hours middle-income parents read to their kids. In her book “Beginning to Read: Thinking and Learning About Print,” author Marilyn Jager Adams had used a study of poor parents that found they read to their kids on average 25 hours before they started school. Adams mentioned that she had read to her child between 1,000 and 1,700 hours in that time. To Adams’ shock, groups from the United Way to Everybody Wins used the comparison as a generalization, saying her example was good for all middle class parents.
600,000: Assaults on campus because of alcohol, according to the National Institute on Alcohol Abuse. But if you look at how the survey defined “assault,” you see that “pushed or hit” was one of the definitions. Getting pushed at a bar is an assault? Alarmist numbers are often inflated by broad definitions of crime, substance abuse and unethical behavior.
35%: Percent of all income tax paid by the top 1 percent of earners. But in surveys, most people tend to underestimate the amount, just as they tend to overestimate the number of illegal immigrants (they’re only 0.3 percent of the US population) and underestimate abortions (335,000 per every million live births in 2006). Political beliefs exaggerate or diminish the perception of issues.
60 degrees: What the average global temperature could rise to because of global warming, according to a 2005 report by climateprediction.net. Unmentioned was that only one simulation resulted in that high a number, while most came in at 37.5 degrees. The latter figure is still an increase, but most reports went with that “wayward tee shot”alarmist figure.